I was going to correct you when, @04:11, you said the area in question was part of two sectors, while it is, of course, only part of the larger sector, but I decided not to. Really GOOD Explanation!! Thank you!
One thing that needs elucidation is from what starting points are the 30 and 150 degree marks. After studying for a while l realized it was from the top of the circles and thence in a clockwise direction. Probably should have been in a counter-clockwise direction to be c I consistent with trigonometry measurements, however either way it needs to be explained. Otherwise, a very good and challenging problem.
I agree. Something I must say is that "Mr Math Man" does good questions but at times quite dodgy diagrams. This is not the first question I've got wrong due to the diagram being misleading. Even in this one, besides the angles, the 2" is a bit misleading - radius or dia? Is the ability to think or read drawings being tested? If you are going to do the outside dia, the 4", as such , do the same for the inner circle. Be consistent.
@@gavindeane3670 Notation - as above, 4in and 2" - consistency please!!!! Also, rather than freak out half the "readers" with inches or the other half with metric, how about just units?
-The 150° marker confuses me. 150° to what? -The inner circle has radius = 2in. -The larger circle has diameter = 4in. -2" radius = 4" diameter so circles are SAME size Conclude the shaded area = 0 volume.
That was my first idea too, so for once I listened to the description of John and got that radius is 2" for the big cirrcle and 1" for the smaller one. 30° from 'North' and 150° from 'North'...
It foxed me too! I assumed the 2 inches referred to a radius, but of what. If it's the whole it's redundant (given the 4 inches diameter) To make any sense I had to assume it was the diameter of the inner circle to get any sensible answer.
I went with the stupid explanation: It's continuous in a clockwise direction, so it's from 30° to 150° from 0°; hence, 120°, i.e. ⅓ of a circle. If I stop to think about it, it's confusing the way he drew it.
@@vespa2860: And yeah, I didn't realize that the 2" was the horizontal line was the diameter of the inner circle at first, as he should have bracketed it in the same manner as the outer circle. I thought he was trying to punk us originally.
The area of the bigger circle = 2^2 x pi = 12,56 (everything in inches^2); the area of the smaller circle = 1 x pi = 3,14. So the area of the complete overlapping area = 12,56 - 3,14 = 9,42. We have to find the sector between 30 degrees and 150 degrees which = 150 degr. - 30 degr. = 120 degr. which is 1/3 x the complete overlapping area (a circle has 360 degr. and 360 : 120 = 3). So the yellow sector = 1/3 x 9,42 is about 3,14 inches^2 or pi inches^2.
I used the center line method. So the center line of the area is a 3" diameter circle x pi / (120/360) x the width of the strip which is 1 inch. Which gives the same answer. Even basic geometry has different paths. In a past life I was an estimator and getting a center line is the key to much applied geometry magic.
I made a comment further up in that the diagram leaves a lot to be desired. The linear dims are badly done but in my case I got messed up by the angles, I managed to confuse where the angles are relative to.
@@goatfiddler8384You didn't confuse where the angles are relative to. The diagram completely fails to tell you, so you had to guess. Perhaps you guessed something different to what the author intended, but that is 100% his fault not yours.
@@MrSummitville math teachers are not trained as engineers, neither as draftsman. Math problems generally need not be exactly to scale. As I wrote above, this diagram only needs to move the 2" label close to the left so that it is clear it is a diameter. John clears this up in the video, but the thumbnail should contain everything needed to solve the problem.
Just like the PEMDAS which is constantly being hammered by this TH-camr, this problem wouldn't cut it in the real world. Maybe in academia those would fly but someone who marked a problem like that would be held accountable for not being clear. If one is calculating trigonometric angles for calculating the sign in those problems, 0 degrees is on the right. Using parentheses and clearly marking the angles, removes all artificial ambiguity from the calculation.
Angle = 150-30 = 120° so 1/3 of the full circle (120/360) Area4 = pi . 2² and Area2 = pi . 1² so the area we are looking for is A = (pi.4 - pi.1)/3 = pi . 3 / 3 = pi inch²
Given any two concentric circles, the annular area is simply defined as pi times the difference of the square of the radii. And in this specific instance, multiplied by the fractional portion of the circle. Those who insist on continually nitpicking the diagram need to step outside into the fresh air.😊
This guy is supposed to be a teacher. It would not have been hard to annotate the diagram properly and there is no excuse for a teacher not to do so. It's not nitpicking the diagram. It's nitpicking the man. And the criticism is fair and correct and appropriate.
The larger circle is 4 inches in diameter, which is radius 2 inches. But the smaller circle is shown as having a radius of 2 inches. Both CANNOT be correct. The set up of the question is incorrect
The 2 inch annotation belongs with the diameter of the smaller circle. But I agree the entire diagram is completely unclear. It's also not obvious where the angles are meant to be measured from. It turns out that they're measured clockwise from the top of the circle, but there is absolutely nothing to indicate that.
@@richardhole8429It is unclear. I wouldn't accept it if someone brought it to me. Where he's written 2" is next to two different lines, one of which (the solid line) is the diameter of the inner circle and the other of which (the dashed line) is the radius of the inner circle. That's just sloppy. And he hasn't labelled the angles at all. That's even worse, given how common it is in mathematics to measure angles anticlockwise from the horizontal yet he turns out to be measuring clockwise from the vertical. This is absolutely basic stuff he's getting wrong. All in all it's a very poor effort. This sort of carelessness is not uncommon in this guy's videos. He can be very shoddy at times.
4in diam and 2" radius, why not write 30° and 150 deg? So the answer to this diagram is zero. Considering the time the OP invested in making the video, I would invest some of it to show an exact diagram with identical length notations.
Solved at 0:29, my answer is pi square inches. I used a calculator, but if I'd fully thought it through first, could have probably done without. Since radius = diameter / 2, and the formula for the area of a circle is pi * radius^2, the areas of the two circles are: large circle = 4 * pi small circle = 1 * pi 4pi - pi = 3pi. Next, the arc covered by 30 deg to 150 deg is 120 deg, or 1/3 of a full circle. Therefore 3pi / 3 = pi.
And now that I've watched the whole video, I still think it makes much more sense to find the areas of the two circles, subtract the smaller from the larger to get the area of the full ring, THEN divide by 3 as the last step instead of dividing each circle's area and then subtract....
@@AyelmarYou made a couple of assumptions that are *not" specified in the drawing. Unfortunately, this is a "gotcha" question and it has more than one valid answer based upon the assumptions the reader makes.
I realise I'm 3 months late, but blimey that's a complicated way of going about it. You don't need to work out the areas of the sectors. Big circle area = 4π inch² Small circle area = π inch² Area between the two = 4π − π = 3π inch² The shaded area is 1/3 of that, so: 3π/3 = π inch²
Area of a circle is pi r^2 Area of big circle = 4 pi Area of small circle = 1 pi 4 pi - 1 pi = 3 pi 120 degrees/360 degrees = 1/3 of the circle 3 pi x 1/3 = 1 pi The shaded area = 1 pi square inches Answer is 22/7 square inches
Could be he did mention the inner circle was diameter 2, not radius 2 within the video, but many viewers do the problem from the screen only without viewing the video, so it is important that all pertinent information be on that screen.
The interior solid line is the diameter of the inner circle and given as 2”, just as the outer solid line indicates that the diameter of the outer circle is 4 inches. The dashed lines serve a very important function - that the beginning and end points of the annular space on both circles lie on the same radii. If they do not, the problem becomes much more difficult.
@@larrydickenson8922 I would suggest that merely moving the label 2" to the left nearer to the edge of the circle would have cleared up the confusion. When it hovers near the circle center, it is unclear what it measures.
The larger issue here is the angle convention. It's easy to see the diameters if you pay attention. But it is impossible to understand the angle with certainty without better labels. There are 2 logical answers for this. One if you believe the regular convention measured w.r.t. x-axis (where 150° should technically be negative). Two, when you arbitrarily guess the authors actual intentions.
@@charlesdougherty9210I recognized the angles in the compass convention right away. I had never seen a math problem use that convention. But wherever the starting point is, from 30 to 150 degrees must be 120.
@@larrydickenson8922The drawing does *NOT* indicate whether the 2" applies to the inner circle diameter (solid line) or the inner circle radius (dashed line). The reader has to guess! These are now "gotcha" type questions. Since he *never* draws to-scale, he could have explained ... the inner radius is 2" therefore the answer is 0 sq-in = a trick question. He is adding ambiguity, which is not acceptable for a math test question.
I just skimmed thru the video and I think John over did it again. All you need is difference between area of 4" and 2" circles for area of the ring. Then 30 to 150 degrees is 1/3 of full circle (120/360), so just divide previous area by 3. I can see some students getting confused by the explanation, although 12 minutes is not bad.
@William - In the old days, there were Analog Clocks. Measuring *clockwise* from "12" to "1" is 30°. But, most schools not longer have Analog Clocks. Mr. Math Man is getting old, too. So now, he has to add ambiguous & misleading labels to his drawings. It's become more of a "gotcha question" than a true math learning / test question. How sad ...
Many of the comments say what i was thinking Especially the 2" if the inner circle has a radius of 2 the the diameter is 4 so the same as the outside circle. If 2" is the diameter it should be drawn that way. The outer circle should have be drawn in proportion to the inner circle.
I don't think the outer circle should have been drawn in proportion. I actually think deliberately drawing diagrams like this NOT to scale is a useful way to exercise the students' abstract thinking and get them to properly focus on the information given. I like the fact that the inner circle is clearly not drawn with half the radius of the outer circle. The problem is with the annotation. It is not clear whether the 2" is meant to apply to the diameter or radius of the inner circle, and he has not indicated where he is measuring the angles from at all.
@@gavindeane3670So, if the circles are *not* drawn to scale, then how are the *angles* drawn to-scale? What if the 30° angle starts at 12 o'clock. But the 150° angle starts at 3 o'clock. *Nothing* stated the angles are drawn to scale and/or have the same startng RAY. The drawing is garbage. Where does it say the inner circle is 2" diameter vs 2" radius? It doesn't. There are many "correct" answers to this ambiguous "gotcha" question. Too many assumptions have to be made by the reader, based on the lack of valid information. This drawing is garbage, at best. If one of our mechanical engineers drew something like this, they would *not* have a job on Monday!
@@MrSummitvilleI literally just said that we need to be told what dimension the 2" label refers to and where the angles are measured. With those issues fixed, the fact that the drawing is not to scale becomes a complete non-issue. You could point out in the question, or even on the diagram itself, that it is not to scale, but that isn't necessary.
This is a very bad diagram imo. The angles look scaled correctly but the diamters are not. At first glance one might instinctively assume it was not to scale. This is potentially confusing. Both angles should be labeled to indicate where the are measured from respectively. Typical convention has us measuring from the x-axis in an anti-clockwise fashion. If that were the case, 30° is roughly where it shoul be, but 150° makes no sense. It would be -150° in typical convention but unfortunately that is not even close to the authors intention. If the problem decides to measure two angles with respect to different starting locations it should be indicated clearly. I would be rather upset if my child were give this on an exam. Great problem, bad diagram.
You're correct on all of that except, I think, the point about it being not too scale. Deliberately drawing diagrams like this not to scale is a good way to exercise the students' abstract thinking and get then to concentrate on the information they've been given. But that must come with a properly annotated diagram. Here he needs to make it clear where the angles are measured from and also what dimension the "2 inch" measurement refers to.
@gavindeane3670 : I would simply ask the teacher. I did that during a bio exam. The question was, "Which wasn't written by Charles Darwin?" One of the answers was, "The Organ of Spices." I walked up to the teacher and quietly asked him, "Is this a typo?" In an equally quiet and flat tone, he said, "No." I kept a stiff upper lip back to my desk. I was the only one out of 400 students to answer the question correctly. When in doubt, don't assume. Ask.
BAD / MISLEADING question. Not at all clear that diameter is 2" for smaller circle from the diagram and if that is then the diagram is not drawn to scale. The actual question is easy to answer for any reasonable 16year old maths student just made harder by poor diagram.
@@terry_willis This is the thing that myself and some others have commented on, the diagram is dodgy so there are multiple ways of interpreting the angles.
@@terry_willisI got 60 degrees too. The diagram does not indicate where the angles are measured from so we have to guess. I guessed that they must be measured anticlockwise from the horizontal axis, because that is such a normal thing to do. So 30 degrees up from the axis, and the only way I could make sense of the 150 degrees was to measure it from the "negative" side of the axis. But of course, John being John he is measuring clockwise from the vertical axis! Like nobody is mathematics does it ever!
@@gavindeane3670 I agree, the diagram is not as clear as it could be, and puzzled me at first. However, the numbered degree markings are at the dotted line radii, which radii mark the ends of the shaded ring, so I figured he was telling us the size of the shaded part compared to the whole circle(s).
That's how I interpreted it too. Turns out he is measuring the angles clockwise from the vertical axis. The fact that we had to try and guess what he meant is the problem.
Got confused with the angle. In trigonometry we start horizontally at zero. Here is the vertical at the top. And I forgot to take the ray instead of the diameter 😢
@@francisdelpuech6415I couldn't see where he was measuring the angles from either. I started from the horizontal too and ended up with a 60 degree sector instead of his 120 degrees.
It really doesn't matter here. We're not doing anything where the system of units matters. Inches, metres, parsecs, angstroms, cubits - it's the same question whatever units he uses. If the choice of units throws you off here, that's definitely your problem not his.
Please Mr Maths Man, can you work on your drawings. Your questions are good to reactivate a brain that has not done maths in ages, but to me, as an Engineer, who has to read drawings, some of the diagrams you use can lead to confusion and a misunderstanding of the question. Other than this gripe, between yourself, Premath and Mind Your Decisions, I'm starting to remove the rust from my maths mind.
John, please do pay attention to this problem. In this case your diagram has multiple difficulties to your students. First, the 2" is unclear to be the radius or the diameter. Second, you are measuring angles from an unusual and unmarked starting point, the y axis. In mathematics we should expect angles to be measured in a standard way, polar coordinates, counterclockwise from the x axis, not compass degrees. Third, mixed units. 4 in and 2". This is sloppy and beneath what a lifelong math teacher should be producing. I, too, am getting old, 73. But, please, keep your standards high.
@@richardhole8429Unfortunately it's not just here where he needs to raise his standards. Some of the mathematical notation he uses in other videos is appalling, and often his mathematics word problems are really sloppy too.
That's what I first thought: 30 degrees up from the horizontal axis, and 150 degrees round from the "negative" side of the horizontal axis, giving a 60 degree sector in total. But no. Turns out he's measuring clockwise from the top.
Show proper diagram.
I was going to correct you when, @04:11, you said the area in question was part of two sectors, while it is, of course, only part of the larger sector, but I decided not to. Really GOOD Explanation!! Thank you!
One thing that needs elucidation is from what starting points are the 30 and 150 degree marks. After studying for a while l realized it was from the top of the circles and thence in a clockwise direction. Probably should have been in a counter-clockwise direction to be c I consistent with trigonometry measurements, however either way it needs to be explained. Otherwise, a very good and challenging problem.
I agree. Something I must say is that "Mr Math Man" does good questions but at times quite dodgy diagrams. This is not the first question I've got wrong due to the diagram being misleading. Even in this one, besides the angles, the 2" is a bit misleading - radius or dia? Is the ability to think or read drawings being tested? If you are going to do the outside dia, the 4", as such , do the same for the inner circle. Be consistent.
@@goatfiddler8384 His mathematics word problems are usually dodgy too. And some of his use of notation is dire.
@@gavindeane3670 Notation - as above, 4in and 2" - consistency please!!!! Also, rather than freak out half the "readers" with inches or the other half with metric, how about just units?
Doesn’t matter where the starting point is. You are only interested in the difference.
@@larrydickenson8922 That only becomes apparent when you realise he's measuring both angles from the same starting point in the same direction.
got it pi areas = 4pi - pi = 3pi 150-30=120 or 1/3 a circle so 3pi / 3 = pi thanks for the fun.
Almost got it right: pi inch² You're welcome!
-The 150° marker confuses me. 150° to what?
-The inner circle has radius = 2in.
-The larger circle has diameter = 4in.
-2" radius = 4" diameter so circles are SAME size
Conclude the shaded area = 0 volume.
That was my first idea too, so for once I listened to the description of John and got that radius is 2" for the big cirrcle and 1" for the smaller one. 30° from 'North' and 150° from 'North'...
Yeah, the angles are not clear at all where he's measuring from.
It foxed me too!
I assumed the 2 inches referred to a radius, but of what. If it's the whole it's redundant (given the 4 inches diameter)
To make any sense I had to assume it was the diameter of the inner circle to get any sensible answer.
I went with the stupid explanation: It's continuous in a clockwise direction, so it's from 30° to 150° from 0°; hence, 120°, i.e. ⅓ of a circle.
If I stop to think about it, it's confusing the way he drew it.
@@vespa2860: And yeah, I didn't realize that the 2" was the horizontal line was the diameter of the inner circle at first, as he should have bracketed it in the same manner as the outer circle. I thought he was trying to punk us originally.
The area of the bigger circle = 2^2 x pi = 12,56 (everything in inches^2); the area of the smaller circle = 1 x pi = 3,14. So the area of the complete overlapping area = 12,56 - 3,14 = 9,42. We have to find the sector between 30 degrees and 150 degrees which = 150 degr. - 30 degr. = 120 degr. which is 1/3 x the complete overlapping area (a circle has 360 degr. and 360 : 120 = 3). So the yellow sector = 1/3 x 9,42 is about 3,14 inches^2 or pi inches^2.
I used the center line method. So the center line of the area is a 3" diameter circle x pi / (120/360) x the width of the strip which is 1 inch. Which gives the same answer.
Even basic geometry has different paths.
In a past life I was an estimator and getting a center line is the key to much applied geometry magic.
I ve started watching your maths helping me lots and actually enjoying maths now x
The radius of the outer circle is 4/2= 2
The radius of the inner circle is also 2.
The area between the two circles is zero.
John, you messed up on this. You meant for the inner circle to have a diameter of 2, but marked the radius as 2.
I made a comment further up in that the diagram leaves a lot to be desired. The linear dims are badly done but in my case I got messed up by the angles, I managed to confuse where the angles are relative to.
@@goatfiddler8384You didn't confuse where the angles are relative to. The diagram completely fails to tell you, so you had to guess. Perhaps you guessed something different to what the author intended, but that is 100% his fault not yours.
The drawing is *garbage* . If any mechanical engineer drew that, he would not have a job on Monday morning
@@MrSummitville math teachers are not trained as engineers, neither as draftsman. Math problems generally need not be exactly to scale. As I wrote above, this diagram only needs to move the 2" label close to the left so that it is clear it is a diameter. John clears this up in the video, but the thumbnail should contain everything needed to solve the problem.
Just like the PEMDAS which is constantly being hammered by this TH-camr, this problem wouldn't cut it in the real world. Maybe in academia those would fly but someone who marked a problem like that would be held accountable for not being clear. If one is calculating trigonometric angles for calculating the sign in those problems, 0 degrees is on the right. Using parentheses and clearly marking the angles, removes all artificial ambiguity from the calculation.
In beginning you said Area of Circle formula was" pi × inches squared ".
It's the radius squared × pi not the diameter..
Excellent channel 👍 Thank you
Angle = 150-30 = 120° so 1/3 of the full circle (120/360)
Area4 = pi . 2² and Area2 = pi . 1² so the area we are looking for is A = (pi.4 - pi.1)/3 = pi . 3 / 3 = pi inch²
Given any two concentric circles, the annular area is simply defined as pi times the difference of the square of the radii. And in this specific instance, multiplied by the fractional portion of the circle. Those who insist on continually nitpicking the diagram need to step outside into the fresh air.😊
This guy is supposed to be a teacher. It would not have been hard to annotate the diagram properly and there is no excuse for a teacher not to do so.
It's not nitpicking the diagram. It's nitpicking the man. And the criticism is fair and correct and appropriate.
The larger circle is 4 inches in diameter, which is radius 2 inches. But the smaller circle is shown as having a radius of 2 inches. Both CANNOT be correct. The set up of the question is incorrect
The 2 inch annotation belongs with the diameter of the smaller circle. But I agree the entire diagram is completely unclear.
It's also not obvious where the angles are meant to be measured from. It turns out that they're measured clockwise from the top of the circle, but there is absolutely nothing to indicate that.
Just listen to the description of the problem...
@@gavindeane3670It is not a bit unclear. The inner circle has a radius of 2, not 1
@@richardhole8429It is unclear. I wouldn't accept it if someone brought it to me. Where he's written 2" is next to two different lines, one of which (the solid line) is the diameter of the inner circle and the other of which (the dashed line) is the radius of the inner circle. That's just sloppy.
And he hasn't labelled the angles at all. That's even worse, given how common it is in mathematics to measure angles anticlockwise from the horizontal yet he turns out to be measuring clockwise from the vertical.
This is absolutely basic stuff he's getting wrong. All in all it's a very poor effort. This sort of carelessness is not uncommon in this guy's videos. He can be very shoddy at times.
4in diam and 2" radius, why not write 30° and 150 deg? So the answer to this diagram is zero. Considering the time the OP invested in making the video, I would invest some of it to show an exact diagram with identical length notations.
Solved at 0:29, my answer is pi square inches. I used a calculator, but if I'd fully thought it through first, could have probably done without.
Since radius = diameter / 2, and the formula for the area of a circle is pi * radius^2, the areas of the two circles are:
large circle = 4 * pi
small circle = 1 * pi
4pi - pi = 3pi.
Next, the arc covered by 30 deg to 150 deg is 120 deg, or 1/3 of a full circle.
Therefore 3pi / 3 = pi.
And now that I've watched the whole video, I still think it makes much more sense to find the areas of the two circles, subtract the smaller from the larger to get the area of the full ring, THEN divide by 3 as the last step instead of dividing each circle's area and then subtract....
@@AyelmarYou made a couple of assumptions that are *not" specified in the drawing. Unfortunately, this is a "gotcha" question and it has more than one valid answer based upon the assumptions the reader makes.
Hmm, the diagram in the thumbnail made it look like the radius of the smaller circle was 2”, confusing
Way too much ambiguity. He is getting old and worn out.
Total area of annulus = pi(4^2-2^2)/4 = 9.424sqin, yellow area by proportion of total annulus= 9.424 x (150-30)/360 = 3.142sqin
Not very bad but not accurate:
Correct answer is pi inch² and not 3.142 inch² but ~ 3.142 inch² will do.
@@panlomitoBased on your *assumptions* , your answer is pi square inches.
I realise I'm 3 months late, but blimey that's a complicated way of going about it. You don't need to work out the areas of the sectors.
Big circle area = 4π inch²
Small circle area = π inch²
Area between the two = 4π − π = 3π inch²
The shaded area is 1/3 of that, so:
3π/3 = π inch²
Area of a circle is pi r^2
Area of big circle = 4 pi
Area of small circle = 1 pi
4 pi - 1 pi = 3 pi
120 degrees/360 degrees = 1/3 of the circle
3 pi x 1/3 = 1 pi
The shaded area = 1 pi square inches
Answer is 22/7 square inches
The answer is π square inches. Why arbitrarily approximate it when it takes fewer characters to write the exact answer?
Thats how I did it 😉
Could be he did mention the inner circle was diameter 2, not radius 2 within the video, but many viewers do the problem from the screen only without viewing the video, so it is important that all pertinent information be on that screen.
The interior solid line is the diameter of the inner circle and given as 2”, just as the outer solid line indicates that the diameter of the outer circle is 4 inches. The dashed lines serve a very important function - that the beginning and end points of the annular space on both circles lie on the same radii. If they do not, the problem becomes much more difficult.
@@larrydickenson8922 I would suggest that merely moving the label 2" to the left nearer to the edge of the circle would have cleared up the confusion. When it hovers near the circle center, it is unclear what it measures.
The larger issue here is the angle convention. It's easy to see the diameters if you pay attention. But it is impossible to understand the angle with certainty without better labels. There are 2 logical answers for this. One if you believe the regular convention measured w.r.t. x-axis (where 150° should technically be negative). Two, when you arbitrarily guess the authors actual intentions.
@@charlesdougherty9210I recognized the angles in the compass convention right away. I had never seen a math problem use that convention. But wherever the starting point is, from 30 to 150 degrees must be 120.
@@larrydickenson8922The drawing does *NOT* indicate whether the 2" applies to the inner circle diameter (solid line) or the inner circle radius (dashed line). The reader has to guess! These are now "gotcha" type questions. Since he *never* draws to-scale, he could have explained ... the inner radius is 2" therefore the answer is 0 sq-in = a trick question. He is adding ambiguity, which is not acceptable for a math test question.
I just skimmed thru the video and I think John over did it again. All you need is difference between area of 4" and 2" circles for area of the ring. Then 30 to 150 degrees is 1/3 of full circle (120/360), so just divide previous area by 3. I can see some students getting confused by the explanation, although 12 minutes is not bad.
Where in trigonometry (or astronomy) have you ever seen angles measured from the zenith, i.e., 12 o'clock position?
And clockwise rather than anticlockwise.
@William - In the old days, there were Analog Clocks. Measuring *clockwise* from "12" to "1" is 30°. But, most schools not longer have Analog Clocks. Mr. Math Man is getting old, too. So now, he has to add ambiguous & misleading labels to his drawings. It's become more of a "gotcha question" than a true math learning / test question. How sad ...
(area of large circle minus area of small circle) / 3 = pi square inches.
30⁰ to 150⁰ equals 120⁰ or 1/3 of the circumference, therefore:
Major circle area - minor circle area × 1/3
((π×4²÷4)−(π×2²÷4))×(1÷3) = 3.1415926.....
Many of the comments say what i was thinking
Especially the 2" if the inner circle has a radius of 2 the the diameter is 4 so the same as the outside circle.
If 2" is the diameter it should be drawn that way.
The outer circle should have be drawn in proportion to the inner circle.
I don't think the outer circle should have been drawn in proportion. I actually think deliberately drawing diagrams like this NOT to scale is a useful way to exercise the students' abstract thinking and get them to properly focus on the information given. I like the fact that the inner circle is clearly not drawn with half the radius of the outer circle.
The problem is with the annotation. It is not clear whether the 2" is meant to apply to the diameter or radius of the inner circle, and he has not indicated where he is measuring the angles from at all.
@@gavindeane3670So, if the circles are *not* drawn to scale, then how are the *angles* drawn to-scale? What if the 30° angle starts at 12 o'clock. But the 150° angle starts at 3 o'clock. *Nothing* stated the angles are drawn to scale and/or have the same startng RAY. The drawing is garbage.
Where does it say the inner circle is 2" diameter vs 2" radius? It doesn't.
There are many "correct" answers to this ambiguous "gotcha" question.
Too many assumptions have to be made by the reader, based on the lack of valid information.
This drawing is garbage, at best. If one of our mechanical engineers drew something like this, they would *not* have a job on Monday!
@@MrSummitvilleI literally just said that we need to be told what dimension the 2" label refers to and where the angles are measured.
With those issues fixed, the fact that the drawing is not to scale becomes a complete non-issue.
You could point out in the question, or even on the diagram itself, that it is not to scale, but that isn't necessary.
This is a very bad diagram imo. The angles look scaled correctly but the diamters are not. At first glance one might instinctively assume it was not to scale. This is potentially confusing. Both angles should be labeled to indicate where the are measured from respectively. Typical convention has us measuring from the x-axis in an anti-clockwise fashion. If that were the case, 30° is roughly where it shoul be, but 150° makes no sense. It would be -150° in typical convention but unfortunately that is not even close to the authors intention. If the problem decides to measure two angles with respect to different starting locations it should be indicated clearly. I would be rather upset if my child were give this on an exam. Great problem, bad diagram.
You're correct on all of that except, I think, the point about it being not too scale.
Deliberately drawing diagrams like this not to scale is a good way to exercise the students' abstract thinking and get then to concentrate on the information they've been given. But that must come with a properly annotated diagram. Here he needs to make it clear where the angles are measured from and also what dimension the "2 inch" measurement refers to.
@gavindeane3670 : I would simply ask the teacher. I did that during a bio exam. The question was, "Which wasn't written by Charles Darwin?" One of the answers was, "The Organ of Spices." I walked up to the teacher and quietly asked him, "Is this a typo?" In an equally quiet and flat tone, he said, "No." I kept a stiff upper lip back to my desk.
I was the only one out of 400 students to answer the question correctly.
When in doubt, don't assume. Ask.
BAD / MISLEADING question.
Not at all clear that diameter is 2" for smaller circle from the diagram and if that is then the diagram is not drawn to scale.
The actual question is easy to answer for any reasonable 16year old maths student just made harder by poor diagram.
Agreed
The angle is 60 degrees not 120 degrees. The correct answer is 1/2 pi or 1.57 sq in
How do you get 60 degrees? 150 - 30 =120.
@@terry_willis This is the thing that myself and some others have commented on, the diagram is dodgy so there are multiple ways of interpreting the angles.
@@terry_willisI got 60 degrees too.
The diagram does not indicate where the angles are measured from so we have to guess. I guessed that they must be measured anticlockwise from the horizontal axis, because that is such a normal thing to do. So 30 degrees up from the axis, and the only way I could make sense of the 150 degrees was to measure it from the "negative" side of the axis.
But of course, John being John he is measuring clockwise from the vertical axis! Like nobody is mathematics does it ever!
@@gavindeane3670 I agree, the diagram is not as clear as it could be, and puzzled me at first. However, the numbered degree markings are at the dotted line radii, which radii mark the ends of the shaded ring, so I figured he was telling us the size of the shaded part compared to the whole circle(s).
pathing an inner−tube of a tyre. whats the area of a scrap piiece of rubber needed
No smiley face for John today. :(
He is getting old and worn out. This is a "gotcha" question, not a math test question. How sad ...
The sweep of this angle is 60° not 120°.
That's how I interpreted it too. Turns out he is measuring the angles clockwise from the vertical axis.
The fact that we had to try and guess what he meant is the problem.
6.28 square units
Got confused with the angle. In trigonometry we start horizontally at zero. Here is the vertical at the top. And I forgot to take the ray instead of the diameter 😢
@@francisdelpuech6415I couldn't see where he was measuring the angles from either. I started from the horizontal too and ended up with a 60 degree sector instead of his 120 degrees.
@@francisdelpuech6415 True, it takes some flexibility to find out John uses compass degrees, so from North.
I take it that your example showing 107° for numbers representing a 60° split is for clickbait.
Mr Math Man is getting old. His drawings are getting worse everyday. Way too many assumptions have to be made by the reader.
Use the metric system
It really doesn't matter here. We're not doing anything where the system of units matters. Inches, metres, parsecs, angstroms, cubits - it's the same question whatever units he uses.
If the choice of units throws you off here, that's definitely your problem not his.
Please Mr Maths Man, can you work on your drawings. Your questions are good to reactivate a brain that has not done maths in ages, but to me, as an Engineer, who has to read drawings, some of the diagrams you use can lead to confusion and a misunderstanding of the question. Other than this gripe, between yourself, Premath and Mind Your Decisions, I'm starting to remove the rust from my maths mind.
John, please do pay attention to this problem. In this case your diagram has multiple difficulties to your students. First, the 2" is unclear to be the radius or the diameter.
Second, you are measuring angles from an unusual and unmarked starting point, the y axis. In mathematics we should expect angles to be measured in a standard way, polar coordinates, counterclockwise from the x axis, not compass degrees.
Third, mixed units. 4 in and 2". This is sloppy and beneath what a lifelong math teacher should be producing.
I, too, am getting old, 73. But, please, keep your standards high.
@@richardhole8429Unfortunately it's not just here where he needs to raise his standards. Some of the mathematical notation he uses in other videos is appalling, and often his mathematics word problems are really sloppy too.
@@gavindeane3670We should note that he has 632,000 followers. That is phenomenal.
pi sq.inches
Did you mean 330?
That's what I first thought: 30 degrees up from the horizontal axis, and 150 degrees round from the "negative" side of the horizontal axis, giving a 60 degree sector in total.
But no. Turns out he's measuring clockwise from the top.
@@gavindeane3670 Appreciated
Garbage